SongEvo simulates the cultural evolution of quantitative traits of bird song. SongEvo is an individual- (agent-) based model. SongEvo is spatially-explicit and can be parameterized with, and tested against, measured song data. Functions are available for model implementation, sensitivity analyses, parameter optimization, model validation, and hypothesis testing.
SongEvo implements the modelpar.sens allows sensitivity analysespar.opt allows parameter optimizationmod.val allows model validationh.test allows hypothesis testinglibrary(SongEvo)
SongEvo implements the model par.sens allows sensitivity analyses par.opt allows parameter optimization mod.val allows model validation h.test allows hypothesis testing
To explore the SongEvo package, we will use a database of songs from Nuttall’s white-crowned sparrow (Zonotrichia leucophrys nuttalli) recorded at three locations in 1969 and 2005.
data("song.data")
Examine global parameters. Global parameters describe our understanding of the system and may be measured or hypothesized. They are called “global” because they are used by many many functions and subroutines within functions. For descriptions of all adjustable parameters, see ?song.data.
data("glo.parms")
glo.parms$mortality.a.m <- glo.parms$mortality.a.f <- glo.parms$mortality.a
glo.parms$mortality.j.m <- glo.parms$mortality.j.f <- glo.parms$mortality.j
glo.parms$male.fledge.n.mean <- glo.parms$male.fledge.n.mean*2
glo.parms$male.fledge.n.sd <- glo.parms$male.fledge.n.sd*2
glo.parms <- glo.parms[!names(glo.parms) %in% c("mortality.a","mortality.j")]
str(glo.parms)
#> List of 17
#> $ learning.error.d : num 0
#> $ learning.error.sd : num 430
#> $ n.territories : num 40
#> $ lifespan : num 2.08
#> $ phys.lim.min : num 1559
#> $ phys.lim.max : num 4364
#> $ male.fledge.n.mean: num 2.7
#> $ male.fledge.n.sd : num 1
#> $ disp.age : num 2
#> $ disp.distance.mean: num 110
#> $ disp.distance.sd : num 100
#> $ terr.turnover : num 0.5
#> $ male.fledge.n : num [1:40] 1 1 2 1 0 2 2 2 2 1 ...
#> $ mortality.a.f : num 0.468
#> $ mortality.a.m : num 0.468
#> $ mortality.j.f : num 0.5
#> $ mortality.j.m : num 0.5
Share global parameters with the global environment. We make these parameters available in the global environment so that we can access them with minimal code.
list2env(glo.parms, globalenv())
#> <environment: R_GlobalEnv>
Data include the population name (Bear Valley, PRBO, or Schooner), year of song recording (1969 or 2005), and the frequency bandwidth of the trill.
str(song.data)
#> 'data.frame': 89 obs. of 3 variables:
#> $ Population: Factor w/ 3 levels "Bear Valley",..: 3 3 3 3 3 3 3 3 3 3 ...
#> $ Year : int 1969 1969 1969 1969 1969 1969 1969 1969 1969 1969 ...
#> $ Trill.FBW : num 3261 2494 2806 2878 2758 ...
SongEvo()In this example, we use songs from individual birds recorded in one population (PRBO) in the year 1969, which we will call starting.trait.
starting.trait <- subset(song.data, Population=="PRBO" & Year==1969)$Trill.FBW
We want a starting population of 40 individuals, so we generate additional trait values to complement those from the existing 30 individuals. Then we create a data frame that includes a row for each individual; we add identification numbers, ages, and geographical coordinates for each individual.
starting.trait2 <- c(starting.trait, rnorm(n.territories-length(starting.trait),
mean=mean(starting.trait), sd=sd(starting.trait)))
init.inds <- data.frame(id = seq(1:n.territories), age = 2, trait = starting.trait2)
init.inds$x1 <- round(runif(n.territories, min=-122.481858, max=-122.447270), digits=8)
init.inds$y1 <- round(runif(n.territories, min=37.787768, max=37.805645), digits=8)
SongEvo() includes several settings, which we specify before running the model. For this example, we run the model for 10 iterations, over 36 years (i.e. 1969–2005). When conducting research with SongEvo(), users will want to increase the number iterations (e.g. to 100 or 1000). Each timestep is one year in this model (i.e. individuals complete all components of the model in 1 year). We specify territory turnover rate here as an example of how to adjust parameter values. We could adjust any other parameter value here also. The learning method specifies that individuals integrate songs heard from adults within the specified integration distance (intigrate.dist, in kilometers). In this example, we do not includ a lifespan, so we assign it NA. In this example, we do not model competition for mates, so specify it as FALSE. Last, specify all as TRUE in order to save data for every single simulated individual because we will use those data later for mapping. If we do not need data for each individual, we set all to FALSE because the all.inds data.frame becomes very large!
iteration <- 10
years <- 36
timestep <- 1
terr.turnover <- 0.5
integrate.dist <- 0.1
lifespan <- NA
mate.comp <- FALSE
prin <- FALSE
all <- TRUE
Now we call SongEvo with our specifications and save it in an object called SongEvo1.
SongEvo1 <- SongEvo(init.inds = init.inds, females = 1.0, iteration = iteration, steps = years,
timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover,
integrate.dist = integrate.dist,
learning.error.d = learning.error.d, learning.error.sd = learning.error.sd,
mortality.a.m = mortality.a.m, mortality.a.f = mortality.a.f,
mortality.j.m = mortality.j.m, mortality.j.f = mortality.j.f, lifespan = lifespan,
phys.lim.min = phys.lim.min, phys.lim.max = phys.lim.max,
male.fledge.n.mean = male.fledge.n.mean, male.fledge.n.sd = male.fledge.n.sd, male.fledge.n = male.fledge.n,
disp.age = disp.age, disp.distance.mean = disp.distance.mean, disp.distance.sd = disp.distance.sd,
mate.comp = mate.comp, prin = prin, all = TRUE)
The model required the following time to run on your computer:
SongEvo1$time
#> user system elapsed
#> 34.846 0.376 36.726
Three main objects hold data regarding the SongEvo model. Additional objects are used temporarily within modules of the model.
First, currently alive individuals are stored in a data frame called “inds.” Values within “inds” are updated throughout each of the iterations of the model, and “inds” can be viewed after the model is completed.
head(SongEvo1$inds, min(5,nrow(SongEvo1$inds)))
#> coordinates id age trait x1 y1
#> M1505 (-122.4528, 37.78974) 1505 9 3391.148 -122.4528 37.78974
#> M1554 (-122.4571, 37.79503) 1554 8 2798.152 -122.4571 37.79503
#> M1590 (-122.4847, 37.80208) 1590 7 2556.961 -122.4847 37.80208
#> M1638 (-122.4606, 37.79375) 1638 6 3836.613 -122.4606 37.79375
#> M1650 (-122.485, 37.80351) 1650 6 3498.137 -122.4850 37.80351
#> male.fledglings female.fledglings territory father sex fitness learn.dir
#> M1505 0 0 0 1448 M 1 0
#> M1554 2 1 1 1491 M 1 0
#> M1590 1 3 1 1507 M 1 0
#> M1638 0 0 0 1532 M 1 0
#> M1650 1 0 1 1581 M 1 0
#> x0 y0
#> M1505 -122.4533 37.79008
#> M1554 -122.4573 37.79486
#> M1590 -122.4813 37.80152
#> M1638 -122.4594 37.79142
#> M1650 -122.4829 37.80469
Second, an array (i.e. a multi-dimensional table) entitled “summary.results” includes population summary values for each time step (dimension 1) in each iteration (dimension 2) of the model. Population summary values are contained in five additional dimensions: population size for each time step of each iteration (“sample.n”), the population mean and variance of the song feature studied (“trait.pop.mean” and “trait.pop.variance”), with associated lower (“lci”) and upper (“uci”) confidence intervals.
dimnames(SongEvo1$summary.results)
#> $iteration
#> [1] "iteration 1" "iteration 2" "iteration 3" "iteration 4" "iteration 5"
#> [6] "iteration 6" "iteration 7" "iteration 8" "iteration 9" "iteration 10"
#>
#> $step
#> [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15"
#> [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
#> [31] "31" "32" "33" "34" "35" "36"
#>
#> $feature
#> [1] "sample.n" "trait.pop.mean" "trait.pop.variance"
#> [4] "lci" "uci"
Third, individual values may optionally be concatenated and saved to one data frame entitled “all.inds.” all.inds can become quite large, and is therefore only recommended if additional data analyses are desired.
head(SongEvo1$all.inds, min(5,nrow(SongEvo1$all.inds)))
#> coordinates id age trait x1 y1 male.fledglings
#> I1.T1.1 (-122.46, 37.78904) 1 2 4004.8 -122.4600 37.78904 1
#> I1.T1.2 (-122.4547, 37.79484) 2 2 3765.0 -122.4547 37.79484 1
#> I1.T1.3 (-122.4525, 37.79513) 3 2 3237.4 -122.4525 37.79513 0
#> I1.T1.4 (-122.4802, 37.79688) 4 2 3621.1 -122.4802 37.79688 1
#> I1.T1.5 (-122.4705, 37.79623) 5 2 3285.4 -122.4705 37.79623 0
#> female.fledglings territory father sex fitness learn.dir x0 y0 timestep
#> I1.T1.1 0 1 0 M 1 0 0 0 1
#> I1.T1.2 0 1 0 M 1 0 0 0 1
#> I1.T1.3 2 1 0 M 1 0 0 0 1
#> I1.T1.4 0 1 0 M 1 0 0 0 1
#> I1.T1.5 0 1 0 M 1 0 0 0 1
#> iteration
#> I1.T1.1 1
#> I1.T1.2 1
#> I1.T1.3 1
#> I1.T1.4 1
#> I1.T1.5 1
We see that the simulated population size remains relatively stable over the course of 36 years. This code uses the summary.results array.
plot(SongEvo1$summary.results[1, , "sample.n"], xlab="Year", ylab="Abundance", type="n",
xaxt="n", ylim=c(0, max(SongEvo1$summary.results[, , "sample.n"], na.rm=TRUE)))
axis(side=1, at=seq(0, 40, by=5), labels=seq(1970, 2010, by=5))
for(p in 1:iteration){
lines(SongEvo1$summary.results[p, , "sample.n"], col="light gray")
}
n.mean <- apply(SongEvo1$summary.results[, , "sample.n"], 2, mean, na.rm=TRUE)
lines(n.mean, col="red")
#Plot 95% quantiles
quant.means <- apply (SongEvo1$summary.results[, , "sample.n"], MARGIN=2, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
lines(quant.means[1,], col="red", lty=2)
lines(quant.means[2,], col="red", lty=2)
Load Hmisc package for plotting functions.
library("Hmisc")
We see that the mean trait values per iteration varied widely, though mean trait values over all iterations remained relatively stable. This code uses the summary.results array.
plot(SongEvo1$summary.results[1, , "trait.pop.mean"], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, 36),
ylim=c(min(SongEvo1$summary.results[, , "trait.pop.mean"], na.rm=TRUE),
max(SongEvo1$summary.results[, , "trait.pop.mean"], na.rm=TRUE)))
for(p in 1:iteration){
lines(SongEvo1$summary.results[p, , "trait.pop.mean"], col="light gray")
}
freq.mean <- apply(SongEvo1$summary.results[, , "trait.pop.mean"], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))#, tcl=-0.25, mgp=c(2,0.5,0))
#Plot 95% quantiles
quant.means <- apply (SongEvo1$summary.results[, , "trait.pop.mean"], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot mean and CI for historic songs.
#plot original song values
library("boot")
#>
#> Attaching package: 'boot'
#> The following object is masked from 'package:survival':
#>
#> aml
#> The following object is masked from 'package:lattice':
#>
#> melanoma
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#text and arrows
text(x=5, y=2720, labels="Historical songs", pos=1)
arrows(x0=5, y0=2750, x1=0.4, y1=mean(starting.trait), length=0.1)
We see that variance for each iteration per year increased in the first few years and then stabilized. This code uses the summary.results array.
#plot variance for each iteration per year
plot(SongEvo1$summary.results[1, , "trait.pop.variance"], xlab="Year",
ylab="Bandwidth Variance (Hz)", type="n", xaxt="n",
ylim=c(min(SongEvo1$summary.results[, , "trait.pop.variance"], na.rm=TRUE),
max(SongEvo1$summary.results[, , "trait.pop.variance"], na.rm=TRUE)))
axis(side=1, at=seq(0, 40, by=5), labels=seq(1970, 2010, by=5))
for(p in 1:iteration){
lines(SongEvo1$summary.results[p, , "trait.pop.variance"], col="light gray")
}
n.mean <- apply(SongEvo1$summary.results[, , "trait.pop.variance"], 2, mean, na.rm=TRUE)
lines(n.mean, col="green")
#Plot 95% quantiles
quant.means <- apply (SongEvo1$summary.results[, , "trait.pop.variance"], MARGIN=2, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
lines(quant.means[1,], col="green", lty=2)
lines(quant.means[2,], col="green", lty=2)
The simulation results include geographical coordinates and are in a standard spatial data format, thus allowing calculation of a wide variety of spatial statistics.
Load packages for making maps.
library("sp")
library("reshape2")
library("lattice")
Convert data frame from long to wide format. This is necessary for making a multi-panel plot.
all.inds1 <- subset(SongEvo1$all.inds, SongEvo1$all.inds$iteration==1)
w <- dcast(as.data.frame(all.inds1), id ~ timestep, value.var="trait", fill=0)
all.inds1w <- merge(all.inds1, w, by="id")
years.SongEvo1 <- (dim(w)[2]-1 )
names(all.inds1w@data)[-(1:length(all.inds1@data))] <-paste("Ts", 1:(dim(w)[2]-1 ), sep="")
Create a function to generate a continuous color palette–we will use the palette in the next call to make color ramp to represent the trait value.
rbPal <- colorRampPalette(c('blue','red')) #Create a function to generate a continuous color palette
Plot maps, including a separate panel for each timestep (each of 36 years). Our example shows that individuals move across the landscape and that regional dialects evolve and move. The x-axis is longitude, the y-axis is latitude, and the color ramp indicates trill bandwidth in Hz.
spplot(all.inds1w[,-c(1:ncol(all.inds1))], as.table=TRUE,
cuts=c(0, seq(from=1500, to=4500, by=10)), ylab="",
col.regions=c("transparent", rbPal(1000)),
#cuts specifies that the first level (e.g. <1500) is transparent.
colorkey=list(
right=list(
fun=draw.colorkey,
args=list(
key=list(
at=seq(1500, 4500, 10),
col=rbPal(1000),
labels=list(
at=c(1500, 2000, 2500, 3000, 3500, 4000, 4500),
labels=c("1500", "2000", "2500", "3000", "3500", "4000", "4500")
)
)
)
)
)
)
In addition, you can plot simpler multi-panel maps that do not take advantage of the spatial data class.
#Lattice plot (not as a spatial frame)
it1 <- subset(SongEvo1$all.inds, iteration==1)
rbPal <- colorRampPalette(c('blue','red')) #Create a function to generate a continuous color palette
it1$Col <- rbPal(10)[as.numeric(cut(it1$trait, breaks = 10))]
xyplot(it1$y1~it1$x1 | it1$timestep, groups=it1$trait, asp="iso", col=it1$Col,
xlab="Longitude", ylab="Latitude")
par.sens()This function allows testing the sensitivity of SongEvo to different parameter values.
par.sens()Here we test the sensitivity of the Acquire a Territory submodel to variation in territory turnover rates, ranging from 0.8–1.2 times the published rate (40–60% of territories turned over). The call for the par.sens function has a format similar to SongEvo. The user specifies the parameter to test and the range of values for that parameter. The function currently allows examination of only one parameter at a time and requires at least two iterations.
parm <- "terr.turnover"
par.range = seq(from=0.4, to=0.6, by=0.025)
sens.results <- NULL
Now we call the par.sens function with our specifications.
extra_parms <- list(init.inds = init.inds,
females = 1, # New in SongEvo v2
timestep = 1,
n.territories = nrow(init.inds),
integrate.dist = 0.1,
lifespan = NA,
terr.turnover = 0.5,
mate.comp = FALSE,
prin = FALSE,
all = TRUE,
# New in SongEvo v2
selectivity = 3,
content.bias = FALSE,
n.content.bias.loc = "all",
content.bias.loc = FALSE,
content.bias.loc.ranges = FALSE,
affected.traits = FALSE,
conformity.bias = FALSE,
prestige.bias=FALSE,
learn.m="default",
learn.f="default",
learning.error.d=0,
learning.error.sd=200)
global_parms_key <- which(!names(glo.parms) %in% names(extra_parms))
extra_parms[names(glo.parms[global_parms_key])]=glo.parms[global_parms_key]
par.sens1 <- par.sens(parm = parm, par.range = par.range,
iteration = iteration, steps = years, mate.comp = FALSE,
fixed_parms=extra_parms[names(extra_parms)!=parm], all = TRUE)
#> [1] "terr.turnover = 0.4"
#> [1] "terr.turnover = 0.425"
#> [1] "terr.turnover = 0.45"
#> [1] "terr.turnover = 0.475"
#> [1] "terr.turnover = 0.5"
#> [1] "terr.turnover = 0.525"
#> [1] "terr.turnover = 0.55"
#> [1] "terr.turnover = 0.575"
#> [1] "terr.turnover = 0.6"
Examine results objects, which include two arrays:
The first array, sens.results, contains the SongEvo model results for each parameter. It has the following dimensions:
dimnames(par.sens1$sens.results)
#> [[1]]
#> [1] "iteration 1" "iteration 2" "iteration 3" "iteration 4" "iteration 5"
#> [6] "iteration 6" "iteration 7" "iteration 8" "iteration 9" "iteration 10"
#>
#> [[2]]
#> [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15"
#> [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
#> [31] "31" "32" "33" "34" "35" "36"
#>
#> [[3]]
#> [1] "sample.n" "trait.pop.mean" "trait.pop.variance"
#> [4] "lci" "uci"
#>
#> [[4]]
#> [1] "par.val 0.4" "par.val 0.425" "par.val 0.45" "par.val 0.475"
#> [5] "par.val 0.5" "par.val 0.525" "par.val 0.55" "par.val 0.575"
#> [9] "par.val 0.6"
The second array, sens.results.diff contains the quantile range of trait values across iterations within a parameter value. It has the following dimensions:
dimnames(par.sens1$sens.results.diff)
#> [[1]]
#> [1] "par.val 0.4" "par.val 0.425" "par.val 0.45" "par.val 0.475"
#> [5] "par.val 0.5" "par.val 0.525" "par.val 0.55" "par.val 0.575"
#> [9] "par.val 0.6"
#>
#> [[2]]
#> [1] "Quantile diff 1" "Quantile diff 2" "Quantile diff 3" "Quantile diff 4"
#> [5] "Quantile diff 5" "Quantile diff 6" "Quantile diff 7" "Quantile diff 8"
#> [9] "Quantile diff 9" "Quantile diff 10" "Quantile diff 11" "Quantile diff 12"
#> [13] "Quantile diff 13" "Quantile diff 14" "Quantile diff 15" "Quantile diff 16"
#> [17] "Quantile diff 17" "Quantile diff 18" "Quantile diff 19" "Quantile diff 20"
#> [21] "Quantile diff 21" "Quantile diff 22" "Quantile diff 23" "Quantile diff 24"
#> [25] "Quantile diff 25" "Quantile diff 26" "Quantile diff 27" "Quantile diff 28"
#> [29] "Quantile diff 29" "Quantile diff 30" "Quantile diff 31" "Quantile diff 32"
#> [33] "Quantile diff 33" "Quantile diff 34" "Quantile diff 35" "Quantile diff 36"
To assess sensitivity of SongEvo to a range of parameter values, plot the range in trait quantiles per year by the parameter value. We see that territory turnover values of 0.4–0.6 provided means and quantile ranges of trill bandwidths that are similar to those obtained with the published estimate of 0.5, indicating that the Acquire a Territory submodel is robust to realistic variation in those parameter values.
In the figure, solid gray and black lines show the quantile range of song frequency per year over all iterations as parameterized with the published territory turnover rate (0.5; thick black line) and a range of values from 0.4 to 0.6 (in steps of 0.05, light to dark gray). Orange lines show the mean and 2.5th and 97.5th quantiles of all quantile ranges.
#plot of range in trait quantiles by year by parameter value
plot(1:years, par.sens1$sens.results.diff[1,], ylim=c(min(par.sens1$sens.results.diff,
na.rm=TRUE), max(par.sens1$sens.results.diff, na.rm=TRUE)), type="l",
ylab="Quantile range (Hz)", xlab="Year", col="transparent", xaxt="n")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))
#Make a continuous color ramp from gray to black
grbkPal <- colorRampPalette(c('gray','black'))
#Plot a line for each parameter value
for(i in 1:length(par.range)){
lines(1:years, par.sens1$sens.results.diff[i,], type="l",
col=grbkPal(length(par.range))[i])
}
#Plot values from published parameter values
lines(1:years, par.sens1$sens.results.diff[2,], type="l", col="black", lwd=4)
#Calculate and plot mean and quantiles
quant.mean <- apply(par.sens1$sens.results.diff, 2, mean, na.rm=TRUE)
lines(quant.mean, col="orange")
#Plot 95% quantiles (which are similar to credible intervals)
#95% quantiles of population means (narrower)
quant.means <- apply (par.sens1$sens.results.diff, MARGIN=2, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
lines(quant.means[1,], col="orange", lty=2)
lines(quant.means[2,], col="orange", lty=2)
par.opt()This function follows par.sens to help users optimize values for imperfectly known parameters for SongEvo. The goals are to maximize accuracy and precision of model prediction. Accuracy is quantified by three different approaches: i) the mean of absolute residuals of the predicted population mean values in relation to target data (e.g. observed or hypothetical values (smaller absolute residuals indicate a more accurate model)), ii) the difference between the bootstrapped mean of predicted population means and the mean of the target data, and iii) the proportion of simulated population trait means that fall within (i.e. are “contained by”) the confidence intervals of the target data (a higher proportion indicates greater accuracy). Precision is measured with the residuals of the predicted population variance to the variance of target data (smaller residuals indicate a more precise model).
target.data <- subset(song.data, Population=="PRBO" & Year==2005)$Trill.FBW
par.opt()Users specify the timestep (“ts”) at which to compare simulated trait values to target trait data (“target.data”) and save the results in an object (called par.opt1 here).
ts <- years
par.opt1 <- par.opt(sens.results=par.sens1$sens.results, ts=ts,
target.data=target.data, par.range=par.range)
Examine results objects (residuals and target match).
par.opt1$Residuals
#> , , Residuals of mean
#>
#> Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5
#> par.val 0.4 246.4130 413.8040 353.52793 228.3723 44.92867
#> par.val 0.425 105.6798 177.1615 78.74531 216.7633 328.67145
#> par.val 0.45 463.4730 182.7290 291.19880 116.4419 322.40075
#> par.val 0.475 133.1587 486.2142 242.81582 147.3633 64.53688
#> par.val 0.5 146.4966 203.1952 345.69295 126.6362 169.09744
#> par.val 0.525 130.7043 463.5629 380.55467 175.0132 427.32781
#> par.val 0.55 515.0104 390.1313 375.29610 279.2949 598.37653
#> par.val 0.575 221.1557 300.7022 351.32024 436.3021 275.19837
#> par.val 0.6 485.2388 324.7634 508.53894 252.0934 52.86032
#> Iteration 6 Iteration 7 Iteration 8 Iteration 9 Iteration 10
#> par.val 0.4 80.55383 163.334018 503.69648 475.1181 214.46314
#> par.val 0.425 257.23840 298.363974 205.01201 202.0157 47.35676
#> par.val 0.45 249.76873 414.336517 258.00770 335.6372 27.72778
#> par.val 0.475 67.55545 145.083835 100.59717 410.7841 216.36051
#> par.val 0.5 11.22704 92.860560 47.68523 361.8775 16.95432
#> par.val 0.525 307.88595 237.245722 91.32073 182.4091 118.16601
#> par.val 0.55 84.59175 192.875941 346.05395 436.0656 277.50271
#> par.val 0.575 368.08224 6.788867 400.76416 218.8793 300.84251
#> par.val 0.6 349.75401 422.699429 502.82968 381.2497 387.17274
#>
#> , , Residuals of variance
#>
#> Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5
#> par.val 0.4 21530.0536 3322.9773 10749.245 20423.455 22316.819
#> par.val 0.425 103.6663 786.6417 14240.197 5064.386 6073.102
#> par.val 0.45 14328.9807 13600.3215 18326.526 9620.973 5221.832
#> par.val 0.475 11800.1313 18040.5555 3458.183 3144.284 5116.635
#> par.val 0.5 3466.4229 432.2343 22378.064 3757.251 4309.797
#> par.val 0.525 8319.5934 4002.2098 11507.068 18115.568 11473.401
#> par.val 0.55 8748.1325 989.9641 16324.034 13305.204 6107.476
#> par.val 0.575 1940.3622 17505.8945 17372.989 11886.316 2038.755
#> par.val 0.6 20177.1138 662.9664 6877.899 5807.582 7179.405
#> Iteration 6 Iteration 7 Iteration 8 Iteration 9 Iteration 10
#> par.val 0.4 9894.1336 11959.124 17772.5949 1167.758 7298.010
#> par.val 0.425 10368.9095 1889.585 2716.8795 16448.251 7702.758
#> par.val 0.45 181.3806 11995.140 5604.6901 15443.614 6930.825
#> par.val 0.475 13965.0800 3119.392 12641.3481 19593.061 1437.361
#> par.val 0.5 8855.5992 10966.088 10719.0423 7866.274 14173.574
#> par.val 0.525 476.0881 2960.649 16272.5787 11133.121 7917.863
#> par.val 0.55 19638.6924 7626.498 6868.2841 523.545 10350.608
#> par.val 0.575 16612.8653 5437.394 256.1759 6442.766 1103.439
#> par.val 0.6 10440.8913 24958.791 5261.3965 3311.034 10498.801
par.opt1$Target.match
#> Difference in means Proportion contained
#> par.val 0.4 263.4354 0.1
#> par.val 0.425 191.7008 0.1
#> par.val 0.45 266.1721 0.1
#> par.val 0.475 201.4470 0.2
#> par.val 0.5 148.7814 0.3
#> par.val 0.525 251.4190 0.0
#> par.val 0.55 349.5199 0.0
#> par.val 0.575 288.0036 0.1
#> par.val 0.6 366.7200 0.1
par.opt()par.opt()plot(par.range, par.opt1$Target.match[,1], type="l", xlab="Parameter range",
ylab="Difference in means (Hz)")
plot(par.range, par.opt1$Prop.contained, type="l", xlab="Parameter range",
ylab="Proportion contained")
res.mean.means <- apply(par.opt1$Residuals[, , 1], MARGIN=1, mean, na.rm=TRUE)
res.mean.quants <- apply (par.opt1$Residuals[, , 1], MARGIN=1, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
plot(par.range, res.mean.means, col="orange", ylim=c(min(par.opt1$Residuals[,,1],
na.rm=TRUE), max(par.opt1$Residuals[,,1], na.rm=TRUE)), type="b",
xlab="Parameter value (territory turnover rate)",
ylab="Residual of trait mean (trill bandwidth, Hz)")
points(par.range, res.mean.quants[1,], col="orange")
points(par.range, res.mean.quants[2,], col="orange")
lines(par.range, res.mean.quants[1,], col="orange", lty=2)
lines(par.range, res.mean.quants[2,], col="orange", lty=2)
par.opt()#Calculate and plot mean and quantiles of residuals of variance of trait values
res.var.mean <- apply(par.opt1$Residuals[, , 2], MARGIN=1, mean, na.rm=TRUE)
res.var.quants <- apply (par.opt1$Residuals[, , 2], MARGIN=1, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
plot(par.range, res.var.mean, col="purple",
ylim=c(min(par.opt1$Residuals[,,2], na.rm=TRUE),
max(par.opt1$Residuals[,,2], na.rm=TRUE)), type="b",
xlab="Parameter value (territory turnover rate)",
ylab="Residual of trait variance (trill bandwidth, Hz)")
points(par.range, res.var.quants[1,], col="purple")
points(par.range, res.var.quants[2,], col="purple")
lines(par.range, res.var.quants[1,], col="purple", lty=2)
lines(par.range, res.var.quants[2,], col="purple", lty=2)
par.opt(): plot trait values for range of parameterspar(mfcol=c(3,2),
mar=c(2.1, 2.1, 0.1, 0.1),
cex=0.8)
for(i in 1:length(par.range)){
plot(par.sens1$sens.results[ , , "trait.pop.mean", ], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, years),
ylim=c(min(par.sens1$sens.results[ , , "trait.pop.mean", ], na.rm=TRUE),
max(par.sens1$sens.results[ , , "trait.pop.mean", ], na.rm=TRUE)))
for(p in 1:iteration){
lines(par.sens1$sens.results[p, , "trait.pop.mean", i], col="light gray")
}
freq.mean <- apply(par.sens1$sens.results[, , "trait.pop.mean", i], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))
#Plot 95% quantiles
quant.means <- apply (par.sens1$sens.results[, , "trait.pop.mean", i], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot mean and CI for historic songs.
#plot original song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#plot current song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_curr <- boot(target.data, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.curr <- boot.ci(boot_curr, conf=0.95, type="basic")
low <- ci.curr$basic[4]
high <- ci.curr$basic[5]
points(years, mean(target.data), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=years, y=mean(target.data), high, low, add=TRUE)
#plot panel title
text(x=3, y=max(par.sens1$sens.results[ , , "trait.pop.mean", ], na.rm=TRUE)-100,
labels=paste("Par = ", par.range[i], sep=""))
}
mod.val()This function allows users to assess the validity of the specified model by testing model performance with a population different from the population used to build the model. The user first runs SongEvo with initial trait values from the validation population. mod.val() uses the summary.results array from SongEvo, along with target values from a specified timestep, to calculate the same three measures of accuracy and one measure of precision that are calculated in par.opt.
We parameterized SongEvo with initial song data from Schooner Bay, CA in 1969, and then compared simulated data to target (i.e. observed) data in 2005.
Prepare initial song data for Schooner Bay.
starting.trait <- subset(song.data, Population=="Schooner" & Year==1969)$Trill.FBW
starting.trait2 <- c(starting.trait, rnorm(n.territories-length(starting.trait),
mean=mean(starting.trait), sd=sd(starting.trait)))
init.inds <- data.frame(id = seq(1:n.territories), age = 2, trait = starting.trait2)
init.inds$x1 <- round(runif(n.territories, min=-122.481858, max=-122.447270), digits=8)
init.inds$y1 <- round(runif(n.territories, min=37.787768, max=37.805645), digits=8)
Specify and call SongEvo() with validation data
iteration <- 10
years <- 36
timestep <- 1
terr.turnover <- 0.5
SongEvo2 <- SongEvo(init.inds = init.inds, females = 1.0, iteration = iteration, steps = years,
timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover,
integrate.dist = integrate.dist,
learning.error.d = learning.error.d, learning.error.sd = learning.error.sd,
mortality.a.m = mortality.a.m, mortality.a.f = mortality.a.f,
mortality.j.m = mortality.j.m, mortality.j.f = mortality.j.f, lifespan = lifespan,
phys.lim.min = phys.lim.min, phys.lim.max = phys.lim.max,
male.fledge.n.mean = male.fledge.n.mean, male.fledge.n.sd = male.fledge.n.sd, male.fledge.n = male.fledge.n,
disp.age = disp.age, disp.distance.mean = disp.distance.mean, disp.distance.sd = disp.distance.sd,
mate.comp = mate.comp, prin = prin, all = TRUE)
Specify and call mod.val()
ts <- 36
target.data <- subset(song.data, Population=="Schooner" & Year==2005)$Trill.FBW
mod.val1 <- mod.val(summary.results=SongEvo2$summary.results, ts=ts,
target.data=target.data)
Plot results from mod.val()
plot(SongEvo2$summary.results[1, , "trait.pop.mean"], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, 36.5),
ylim=c(min(SongEvo2$summary.results[, , "trait.pop.mean"], na.rm=TRUE),
max(SongEvo2$summary.results[, , "trait.pop.mean"], na.rm=TRUE)))
for(p in 1:iteration){
lines(SongEvo2$summary.results[p, , "trait.pop.mean"], col="light gray")
}
freq.mean <- apply(SongEvo2$summary.results[, , "trait.pop.mean"], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))
#Plot 95% quantiles
quant.means <- apply (SongEvo2$summary.results[, , "trait.pop.mean"], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot mean and CI for historic songs.
#plot original song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#text and arrows
text(x=5, y=2720, labels="Historical songs", pos=1)
arrows(x0=5, y0=2750, x1=0.4, y1=mean(starting.trait), length=0.1)
#plot current song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_curr <- boot(target.data, statistic=sample.mean, R=100)
ci.curr <- boot.ci(boot_curr, conf=0.95, type="basic")
low <- ci.curr$basic[4]
high <- ci.curr$basic[5]
points(years, mean(target.data), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=years, y=mean(target.data), high, low, add=TRUE)
#text and arrows
text(x=25, y=3100, labels="Current songs", pos=3)
arrows(x0=25, y0=3300, x1=36, y1=mean(target.data), length=0.1)
The model did reasonably well predicting trait evolution in the validation population, suggesting that it is valid for our purposes: the mean bandwidth was abs(mean(target.data)-freq.mean)Hz from the observed values, ~21% of predicted population means fell within the 95% confidence intervals of the observed data, and residuals of means (~545 Hz) and variances (~415181 Hz) were similar to those produced by the training data set.
h.test()This function allows hypothesis testing with SongEvo. To test if measured songs from two time points evolved through mechanisms described in the model (e.g. drift or selection), users initialize the model with historical data, parameterize the model based on their understanding of the mechanisms, and test if subsequently observed or predicted data match the simulated data. The output data list includes two measures of accuracy: the proportion of observed points that fall within the confidence intervals of the simulated data and the residuals between simulated and observed population trait means. Precision is measured as the residuals between simulated and observed population trait variances. We tested the hypothesis that songs of Z. l. nuttalli in Bear Valley, CA evolved through cultural drift from 1969 to 2005.
Prepare initial song data for Bear Valley.
starting.trait <- subset(song.data, Population=="Bear Valley" & Year==1969)$Trill.FBW
starting.trait2 <- c(starting.trait, rnorm(n.territories-length(starting.trait),
mean=mean(starting.trait), sd=sd(starting.trait)))
init.inds <- data.frame(id = seq(1:n.territories), age = 2, trait = starting.trait2)
init.inds$x1 <- round(runif(n.territories, min=-122.481858, max=-122.447270), digits=8)
init.inds$y1 <- round(runif(n.territories, min=37.787768, max=37.805645), digits=8)
Specify and call SongEvo() with test data
SongEvo3 <- SongEvo(init.inds = init.inds, females = 1.0, iteration = iteration, steps = years,
timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover,
integrate.dist = integrate.dist,
learning.error.d = learning.error.d, learning.error.sd = learning.error.sd,
mortality.a.m = mortality.a.m, mortality.a.f = mortality.a.f,
mortality.j.m = mortality.j.m, mortality.j.f = mortality.j.f, lifespan = lifespan,
phys.lim.min = phys.lim.min, phys.lim.max = phys.lim.max,
male.fledge.n.mean = male.fledge.n.mean, male.fledge.n.sd = male.fledge.n.sd, male.fledge.n = male.fledge.n,
disp.age = disp.age, disp.distance.mean = disp.distance.mean, disp.distance.sd = disp.distance.sd,
mate.comp = mate.comp, prin = prin, all = TRUE)
Specify and call h.test()
target.data <- subset(song.data, Population=="Bear Valley" & Year==2005)$Trill.FBW
h.test1 <- h.test(summary.results=SongEvo3$summary.results, ts=ts,
target.data=target.data)
The output data list includes two measures of accuracy: the proportion of observed points that fall within the confidence intervals of the simulated data and the residuals between simulated and observed population trait means. Precision is measured as the residuals between simulated and observed population trait variances.
Eighty percent of the observed data fell within the central 95% of the simulated values, providing support for the hypothesis that cultural drift as described in this model is sufficient to describe the evolution of trill frequency bandwidth in this population.
h.test1
#> $Residuals
#> Residuals of mean Residuals of variance
#> Iteration 1 282.7422 39322.937
#> Iteration 2 148.6220 84015.469
#> Iteration 3 395.0178 7819.765
#> Iteration 4 767.7079 25738.780
#> Iteration 5 703.9459 73787.439
#> Iteration 6 366.8346 40452.348
#> Iteration 7 690.2566 5652.871
#> Iteration 8 387.9328 30003.637
#> Iteration 9 357.9436 150133.050
#> Iteration 10 506.9128 8890.607
#>
#> $Prop.contained
#> [1] 0.4
We can plot simulated data in relation to measured data.
#Plot
plot(SongEvo3$summary.results[1, , "trait.pop.mean"], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, 35.5),
ylim=c(min(SongEvo3$summary.results[, , "trait.pop.mean"], na.rm=TRUE),
max(SongEvo3$summary.results[, , "trait.pop.mean"], na.rm=TRUE)))
for(p in 1:iteration){
lines(SongEvo3$summary.results[p, , "trait.pop.mean"], col="light gray")
}
freq.mean <- apply(SongEvo3$summary.results[, , "trait.pop.mean"], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))#, tcl=-0.25, mgp=c(2,0.5,0))
#Plot 95% quantiles (which are similar to credible intervals)
quant.means <- apply (SongEvo3$summary.results[, , "trait.pop.mean"], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot original song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#plot current song values
points(rep(ts, length(target.data)), target.data)
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_curr <- boot(target.data, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.curr <- boot.ci(boot_curr, conf=0.95, type="basic")
low <- ci.curr$basic[4]
high <- ci.curr$basic[5]
points(years, mean(target.data), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=years, y=mean(target.data), high, low, add=TRUE)
#text and arrows
text(x=11, y=2850, labels="Historical songs", pos=1)
arrows(x0=5, y0=2750, x1=0.4, y1=mean(starting.trait), length=0.1)
text(x=25, y=2900, labels="Current songs", pos=1)
arrows(x0=25, y0=2920, x1=years, y1=mean(target.data), length=0.1)